Puzzle



April 20, 1943.. H. w. HUTcHlsoN PUZZLE Filed Sept. 27, 1941 Patented Apr. 2o, 1943 UNITED STATES PATENT OFFICE PUZZLE Harold W. Hutchison, Miami, Fla.

Application September 27, 1941, Serial No. 412,641

7 Claims.

This invention relates to a puzzle, and more particularly to a puzzle in which a plurality of geometrical pieces are to Ybe assembled to fit within a prescribed area.

The principal object of the invention is to provide a puzzle in which the pieces when assembled, except in one particular manner, cover an area greater than the prescribed area into which they must fit to solve the puzzle.

Another object is the provision of puzzle xpieces which present to the eye the illusion of being regular geometric figures, when in fact the pieces are slightly distorted to create certain chords of the ligure which are shorter lthan other chords. The cumulative effect of the shorter chords, when the pieces are assembled with the ends of the short chords of adjacent pieces in coincidence, is such that the assembled pieces will 'fit intoa much smaller area than would appear possible.

A further object is Ato provide a puzzle involving well -known geometric principles and depending Vupon optical illusion to make the solution unobvious.

'Other objects will be disclosed in the following detailed description and claims forming part of this application.

Referring now to the drawing, throughout the several figures of which the same characters of reference have been employed to designate identical parts:

Figure 1 is a plan Vview of a puzzle embodying the principles of the present invention, the pieces being shown in assembled position;

Figure 2 is a vertical section taken on the line 2 2 of Figure 1;

Figure 3 is a diagrammatic View showing the method of laying out a puzzle piece as well as disclosing the geometric principles upon which the puzzle is based; and

Figure 4 is a view of another form in which the puzzle pieces may be made.

In the drawing, numeral v5 designates a puzzle or game board having an annular recess 6 in which a plurality of puzzle pieces 'l are to be assembled.

It should be understood at the outset, that the shape of the recess y6 need not necessarily be circular but maybe of other shape, such as va polygon similar to the puzzle Vpieces used. It should also be understood that the puzzle pieces may be made in any polygonal shape up to and including the limit of polygons, which is a circle,

although -polygons having Ian y'even number of faces lend themselves more perfectly to the practice of the invention than do those having an uneven number.

For purposes of illustration, the recess 6 is shown as being annular, and the puzzle pieces 'l of two forms, octagonal and circular.

It is a well known geometrical fact that, If the circumference of a circle is divided into any number of equal parts, tangents drawn at the point of division form a regular circumscribed polygon. A regular polygon vis both equilateral and equiangular.

In designing a puzzle piece 'l of octagonal shape, a circle 8 with X'as its center must rst be drawn, and divided into eight equal parts as shown by the points of division A, B, C, D, E, F, G, and H in Figure 3. Tangents KL, LM, MN, OP, PQ and QR are then drawn to the circle at the points A, B, C, E, F and G, thus forming six sides of a regular Octagon. The seventh side NO of the figure connecting the sides MN and OP is drawn parallel to a tangent through` D but moved slightly inwardly toward the center so that a portion of the line NO subtends an arc of the circle.

The distance which the side NO is moved inward from the circumference of the circle -is arbitrary, but it has lbeen found that in pieces of octagonal shape l@ of an inch is sufficient for the purpose, and at the same time slight enough to carry out the illusion that the resultant octagon is regular.

The eighth side RK connecting the sides QR and KL could be drawn tangent to the circle through the point H, but to further the illusion of regularity of the polygon, it is drawn parallel to such a tangent but outside the circumference of the circle a distance equal to that which the side NO is moved inward. This provides an Octagon in Which all diameters between parallel faces are of equal length, and in which all diagonals from corner to corner are equal.

The fact that the sides NO and RK are parallel to tangents to the -circle but not coincident therewith, results in a polygon whichis equiangular but not equilateral; the side NO being longer, and the side RK being lshorter than the regular sides. To make this inequality inobvous to the eye, the corners at'the junctures of the sides are rounded to eliminate sharp points from which measurements could be taken.

In a regular polygon all apothems are equal. Thus in Figure 3 the apothems AX and FX are equal for they are drawn to regular sides of the polygon and are Vradii of .the inscribed circle. As 'has been described, the center portion uf the side NO subtends an arc of the circle and, therefore, the apothem XI to this side is shorter than the radius of the circle and shorter than any apothem to a regular side.

If chords AF and AI are drawn, they will form the third sides of the triangles AXF and AIU, respectively. The chord AF connecting the extremities of apothems to regular sides of the polygon is representativeof any chord to a regular polygon, while the chord AI is representaf tive of a chord connecting the extremities of a regular apothem and the short apothem XI of which there are two AI and GI. In the triangles AXF and AXI, side AX is common to both, side angles AXF and AXD are equal, which results l in the chord AI being shorter than the chord AF. In otherwords, chords AI and GI Ywhich intersect the irregular side NO are shorter than any of the regular chords of the polygon.

Theprovision of a puzzle piece of geometrical outline having aV chord shorter than the other chords of the figure is the principle upon which this invention is based. i

A plurality of such pieces 'l are provided, to be assembled within the recess 6 in the puzzle board 5. The annular recess 6 is of such size that if the pieces 'I are placed in the recess with the faces at the ends of a regular chord, such as AF, in contact with like faces of adjacent pieces, the recess will be too small to accommodate the pieces. If, however, the pieces are assembled with the faces at the ends of the short chords in contact Vwith like faces of adjacent pieces, the pieces Will t perfectly into the recess.

The reason for this can .best be understood by reference to Figure 1 in which the pieces are shown assembled and the short chords are indicated by dotted lines. It can be seen that the chords represent the straight line distance between puzzle pieces. If the pieces are so arranged that the short chords bridge this distance, the aggregate or total length of the combined chords will be much less than if the regular or longer chords were in this position, and the pieces may be assembled within a smaller area.

Due to the fact that the puzzle pieces appear to be of regular geometrical shape, a player in attempting to solve the puzzle must necessarily experiment with the pieces, turning them about until he iinally succeeds in placing each ofthe pieces with its short chord bridging the distance between adjacent pieces, at which time the pieces will t the recess and the puzzle will be solved.

In Figure 4 is shown a second forni of puzzle piece 8. In this form the outline of the piece is a circle, slightly distorted in a manner similar tothe distortion of the polygon to provide a short chord YZ. It is obvious that theV same conditions prevail in a puzzle having pieces of this shape as exist when polygonal pieces are used. Many variations are possible in both the shape of the confining recess and the shape ofthe puzzle pieces, as long as the pieces have certain which are equiangular lbut not equilateral; each puzzle piece having a plurality of sides which are sides of a regular polygon, one irregular side which is closer to the center of the puzzle piece than the regular sides, and a second irregular side opposite to the iirst and further removed from the center than the regular sides, whereby all diameters between opposite faces are equal, all diagonals from corner to corner are equal, and a chord from the center of the first irregular side to Vthe center of a regular side is shorter than similar chords between two regular sides;

said predetermined areal on the puzzle board being too small to permit assembling the puzzle pieces within its confines in any position except XF is greater than side XI, and the included" with the short chord of each puZZle P1608 bridging the distance between adjacent puzzle pieces. 2. A puzzle comprising, a puzzle board having thereon a closed area and a plurality of congruent puzzle pieces of geometric shape, the shape of each piece being regular for the major portion of its periphery and slightly irregular for a minor portion, said area being too small to permit assembling the puzzle pieces within its contines except when the pieces are arranged with the irregular portion of each piece in contact with the periphery of an adjacent piece.

3. A puzzle comprising, a puzzle board having thereon a closed area and a plurality of congruent puzzle pieces of geometric shape, the shape of each piece being regular for the major portion of its periphery and slightlyirregular for a minor portion, said irregular portion being closer to the center of regularity of the piece than said regular portion, said area being too small to permit assembling the puzzle pieces withinits connes except when the pieces are arranged with the irregular portion of each piece in contact with the periphery of an adjacent piece.

4. A puzzle comprising, a puzzle board having thereon a closed area, and a plurality of congruent puzzle pieces of regular polygonal shape for Vthe major portion of the periphery, and having at least one irregular side, said irregular side being closer to the center of regularity than the regular sides, said puzzle `pieces being of such size as to fit together in a closed series Within said area, with portions of their peripheries contacting the perimeter of said area Vonly when their said irregular sides are in contact With adjacent pieces.

5. A puzzle comprising, a puzzle board having thereon a closed area of uniform width defined between inner and outer perimeters, and aplurality of congruent puzzle pieces of regular polygonal shape for the majorr portion of the periphery, and having at least one irregularslde, said irregular side being closer to-the center of regularity than the regular sides, said puzzle pieces being of such size as to t together. in a closed series within said area, with portions of their peripheries contacting the inner and outer perimeters of said area only when their saidirregular sides are in contact with adjacent pieces.

6. A puzzle comprising, a puzzle board having thereon a closed area and a plurality 'oflcongruent puzzle pieces circular for the major portion of the periphery, of non-circular curvature for a minor portion, said minor portion being closer to the center of regularity than the major portion, said puzzle pieces being of such size as to t together in a closed series within 'said area with portions of their peripheries contacting the perimeter of said area only when ltheir said noncircular portions are ,in contact with adjacent pieces. f

7. A puzzle comprising, a puzzle board having thereon a. closed area of uniform Width defined between inner and outer perimeters, and a plurality of congruent puzzle pieces circular for the major portion of the periphery, of non-circular curvature for a minor portion, said minor portion being closer to the center of regularity than the major portion, said puzzle pieces being of such size as to t together in a closed series Within said area with portions of their peripheries contacting the inner and outer perimeters of said area only when their said non-circular portions are in contact with adjacent pieces.

HAROLD W. HUTCHISON. 

